Solve for $x$ and $y$ using substitution. ${x+2y = 4}$ ${y = -5x+11}$
Solution: Since $y$ has already been solved for, substitute $-5x+11$ for $y$ in the first equation. ${x + 2}{(-5x+11)}{= 4}$ Simplify and solve for $x$ $x-10x + 22 = 4$ $-9x+22 = 4$ $-9x+22{-22} = 4{-22}$ $-9x = -18$ $\dfrac{-9x}{{-9}} = \dfrac{-18}{{-9}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = -5x+11}\thinspace$ to find $y$ ${y = -5}{(2)}{ + 11}$ $y = -10 + 11$ $y = 1$ You can also plug ${x = 2}$ into $\thinspace {x+2y = 4}\thinspace$ and get the same answer for $y$ : ${(2)}{ + 2y = 4}$ ${y = 1}$